Business Process Modelling based on Petri nets

. Business process modelling is the way business processes are expressed. Business process modelling is the foundation of business process analysis, reengineering, reorganization and optimization. It can not only help enterprises to achieve internal information system integration and reuse, but also help enterprises to achieve with the external collaboration. Based on the prototype Petri net, this paper adds time and cost factors to form an extended generalized stochastic Petri net. It is a formal description of the business process. The semi-formalized business process modelling algorithm based on Petri nets is proposed. Finally, The case from a logistics company proved that the modelling algorithm is correct and effective.


INTRODUCTION
Business process everywhere, to improve the business process management and processing capabilities has very important significance to improve work efficiency for the government and to improve business performance for the enterprise.With the development of information technology, it creates the technical foundation for a substantial increase for business process management capabilities and processing power [1].
Business process modelling is the way business processes are expressed.Business process modelling is the foundation of business process analysis, reengineering, reorganization and optimization.The common modelling languages include UML [2],EPC[3],Workflow Graph [4],BPMN [5], Pi-Calculus [6] and Pet nets [7].Petri is not only intuitive, but also a formal definition.Based on the prototype Petri net, this paper adds time and cost factors to form an extended generalized stochastic Petri net.It is a formal description of the business process.The semiformalized business process modelling algorithm based on Petri nets is proposed.The Φ is empty.× is the two-set (space) of the Cartesian product operation, so F is the set of ordered pair composed of a C element and a A element.dom (F) is the order dual of F contains the first element (starting) of the set, cod (F) is the second element (the end) of the collection: dom (F) = {x | y: (x, y) ∈ F}; cod (F) = {x | y: (y, x) ∈ F}.Net standard graphics is that circle represents the condition, with the box that transition s from x to y by a directed arc (arrow) that ordered dual (x, y).(hence (x, y) ∈F), it is also known as directed arcs).Definition 2.2 Satisfy the following six conditions set Σ = (C, A, F, M,  , g ) is called a business process system:

DEFINITION OF BUSINESS PROCESS
where T is divided into time transition Set At and instantaneous transition set Ai 2 sub-sets.The implementation of the time transition will take some time, the instantaneous transition implementation time is negligible, that is, A=At ∪ Ai , At ∩ Ai ≠Φ; (3) F in the permitted inhibitor arcs, inhibitor arcs exist only from the position to transition the arc.Inhibitor arcs can be implemented by the conditions of the original link becomes unenforceable (disable) the conditions, the original nonimplementation of the conditions can be implemented into the conditions, and transition in the linked implementation, not marked out from the connected position; (4)  ={  1,  2, …  m},  i is the average implementation rate of the transition ai (ai ∈ A), which represents average implementation times in the case of the implementation in unit time.The unit is times/hour; (5) g={g1,g2,…,gm}, gi is the average implementation costs of the transition ai (ai ∈ A), which represents implemented cost in the case of implementation per unit time, The unit is the yuan/hour.. Formally, C={c1, c2, c3, c4}, At={ ei, ej}, Ai={e0,en}, A={e0, ei, ej, en}, F={(e0, c1), (e0, c2), (c1, ei) ,(c2, ej), (ei, c3), (ej, c4), (c3, en), (c4, en)}, Ae={e0}, Ax={en}.

BUSINESS PROCESS MODELLING
Business process modelling method is from top to bottom, and gradually decomposed.The first step in any business process is to create an initial block and the definition of the initial block is shown in Figure 5. Business process by layer refinement, the modeler can get a business process to meet their needs model.The modelling of business processes is described in Function 3.1.Two sub-functions are called in the process of business process modelling.Function 3.2 is used for business process layer by layer decomposition and refinement.Function 3.3 is used to establish a link between non-adjacent libraries in a business process.

CONCLUSIONS
In this paper, the concept of cost is introduced to the generalized stochastic Petri nets.It is called it extended generalized stochastic Petri nets.At the same time, basic block is introduced to business process modelling.Business process is got described with the extended stochastic Petri net.The semi-formalized business process modelling algorithm based on Petri nets is proposed.Finally, the case from a logistics company proved that the modelling algorithm is correct and effective.

Definition 2 . 1 [ 7 ]
A triple N=(C, A, F) is called a net if (1)C∪A ≠Φ; (2)C∩A=Φ; (3)F⊆(C×A)∪(A×C) is a binary relation, the flow relation of N; (4) dom(F)∪cod(F)=C∪A.C which is called the condition set of N, A is called the activity set, F is called arc set.X = C ∪ A is called the N element set.Elements in C are called the condition or element C, Elements in A are called activity or element A.

Figure 7 .
Figure 7. Extended generalized stochastic Petri net representation of business processes